Aron, Richard M.; Seoane-Sepúlveda, Juan B. Algebrability of the set of everywhere surjective functions on \(\mathbb C\). (English) Zbl 1130.46013 Bull. Belg. Math. Soc. - Simon Stevin 14, No. 1, 25-31 (2007). Summary: We show that the set \(\mathcal L\) of complex-valued everywhere surjective functions on \(\mathbb C\) is algebrable. Specifically, \(\mathcal L\) contains an infinitely generated algebra every nonzero element of which is everywhere surjective. We also give a technique to construct, for every \(n\in\mathbb N\), \(n\) algebraically independent everywhere surjective functions, \(f_1,f_2,\dots,f_n\), so that for every non-constant polynomial \(P\in\mathbb C[z_1,\dots,z_n]\), \(P(f_1,f_2,\dots,f_n)\) is also everywhere surjective. Cited in 52 Documents MSC: 46E25 Rings and algebras of continuous, differentiable or analytic functions 15A03 Vector spaces, linear dependence, rank, lineability PDFBibTeX XMLCite \textit{R. M. Aron} and \textit{J. B. Seoane-Sepúlveda}, Bull. Belg. Math. Soc. - Simon Stevin 14, No. 1, 25--31 (2007; Zbl 1130.46013) Full Text: Euclid